2025/11/11 by Yakov Shlapentokh-Rothman, Shlapentokh-Rothman, Yakov, Mihai Tohaneanu +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2511.08751
openalex publication_date 2025/11/11 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28
On the full range of sub-extremal Kerr exterior spacetimes we give a new proof of energy boundedness for high-frequency projections of solutions to the wave equation onto trapped frequencies. A key feature of the new estimate is that it circumvents the use of an integrated local energy decay (ILED) statement. As an illustration of the robustness of the estimate, we use it to establish energy boundedness for solutions to the wave equation on stationary and axisymmetric metrics which are merely C1 close to a sub-extremal Kerr spacetime. We show explicitly that such perturbed metrics may possess stably trapped null geodesics, and thus one does not expect ILED statements to hold.